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ECE 5233 Satellite Communications

ECE 5233 Satellite Communications. Prepared by: Dr . Ivica Kostanic Lecture 4: Look angle determination (Section 2.2). Spring 2014. Outline . Sub-satellite point Motion of sub-satellite point Calculation of elevation and azimuth Look angle calculation spreadsheet

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ECE 5233 Satellite Communications

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  1. ECE 5233 Satellite Communications Prepared by: Dr. Ivica Kostanic Lecture 4: Look angle determination (Section 2.2) Spring 2014

  2. Outline • Sub-satellite point • Motion of sub-satellite point • Calculation of elevation and azimuth • Look angle calculation spreadsheet • Look angles to geo-synchronous satellites • Examples Important note: Slides present summary of the results. Detailed derivations are given in notes.

  3. Sub-satellite point • Point at which a line between the satellite and the center of the Earth intersects the Earth’s surface • Location of the point expressed in terms of latitude and longitude • If one is in the US it is common to use • Latitude – degrees north from equator • Longitude – degrees west of the Greenwich meridian • Location of the sub satellite point may be calculated from coordinates of the rotating system as:

  4. Examples of sub-satellite point trajectories • sub-satellite point used for 2D map display of satellite path • For most satellites the trajectory is part of sinusoidal • For geo-stationary satellites the trajectory is a point Sirius radio – two geo stationary and three highly inclined orbit satellites Note: maps are generated using STK by Analytic Graphics, Inc. International space station – LEO orbit

  5. Look angles – elevation (El) and azimuth (Az) • Az – angular distance of the satellite from the north • Az is between 0 and 360 degrees • El – angular distance of the satellite from the local horizontal plane • El is between 0 and 90 degrees • Az and El are required for proper pointing of the Earth station antenna • If the satellite is geo-stationary the antenna is pointed once • If the satellite is on non stationary orbit, the ground system needs to track the Az and El in time Definition of Az and El

  6. Calculation of elevation Given: Le – latitude of Earth Station le – longitude of Earth station Ls – latitude of sub-satellite point ls – longitude of sub-satellite point rs – distance to satellite Example: Calculate El for the following data ES: latitude: 28.06280 N (+0.4898 rad) longitude: 80.62311 W (+1.4071 rad) SSP: latitude: 49.5432 N (+0.8647 rad) longitude: 48.2967W (+0.8429 rad) radius, rs = 38000km Step 1: Step 1: Step 2: Step 2: Where re is the radius of the Earth (6370km)

  7. Calculation of azimuth - cases • Eight cases to consider • Northern hemisphere – 4 cases • At least one of the two points (Earth station, sub-satellite point) is in the northern hemisphere • Southern hemisphere – 4 cases • Both points (Earth station and sub-satellite point) are in the southern hemisphere Given: Le – latitude of Earth Station le – longitude of Earth station Ls – latitude of sub-satellite point ls – longitude of sub-satellite point rs – distance to satellite Note: presented algorithm accommodates general case

  8. Calculation of azimuth – northern hemisphere where B west of A A west of B Note: B chosen to be north of A Solve tan equations for X and Y Identify the case and use table to determine the AZ SSP- sub-satellite point ES – Earth station

  9. Calculation of azimuth – southern hemisphere where B west of A A west of B Note: B chosen to be south of A Solve tan equations for X and Y Identify the case and use table to determine the AZ SSP- sub-satellite point ES – Earth station

  10. Azimuth calculation - example Example: Calculate Az for the following data ES: latitude: 28.06280 N (+0.4898 rad) longitude: 80.62311 W (-1.4071 rad) SSP: latitude: 49.5432 N (+0.8647 rad) longitude: 48.2967W (-0.8429 rad) radius, rs = 6738km This is Case 2 of Northern hemisphere calculation: C = |80.62311-48.2967|=32.326410.5642 rad LB=49.54320.8647 rad LA=28.06280.4898 rad tan[0.5(Y-X)]=0.82510.5(Y-X)=0.6898 rad tan[0.5(Y+X)]=5.41000.5(Y-X)=1.3880 rad X=0.6982 rad Y=2.0778 rad For Case 2 of northern hemisphere: Az = X = 0.6982 rad40.0016

  11. Look angle worksheet

  12. Look angles to geo-stationary satellites • Geo stationary satellites • Occupy non-inclined geo-synchronous orbit • Always above same equatorial point • Location specified using longitude of the sub-satellite point and distance to the satellite • The El/Az calculation spreadsheet “works” for geo-stationary satellites • There are also many websites that calculate El/Az pairs • Example site: http://www.sadoun.com/Sat/Installation/Satellite-Heading-Calculator.htm • VSAT broadcast terminals are usually operating with Geo-stationary satellites Example of “dish pointer” website Note: compare pointing results between class spreadsheet and dish-pointing websites

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